Respuesta :
Answer:
Ques 1)
[tex]g(x)=-12x+48[/tex]
Ques 2)
[tex]g(x)=|3x|+4[/tex]
Step-by-step explanation:
Ques 1)
We know that if a graph is stretched by a factor of a then the transformation if given by:
f(x) → a f(x)
Also, we know that the translation of a function k units to the right or to the left is given by:
f(x) → f(x+k)
where if k>0 then the shift is k units to the left
and if k<0 then the shift is k units to the right.
Here the graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 units and a translation of 4 units right.
This means that the function g(x) is given by:
[tex]g(x)=4f(x-4)\\\\i.e.\\\\g(x)=4(-3(x-4))\\\\i.e.\\\\g(x)=-12(x-4)\\\\i.e.\\\\g(x)=-12x+48[/tex]
Ques 2)
We know that the transformation of the type:
f(x) → f(x)+k
is a shift or translation of the function k units up or down depending on k.
If k>0 then the shift is k units up.
and if k<0 then the shift is k units down.
Here, The graph of the function f(x)=|3x| is translated 4 units up.
This means that the transformed function g(x) is given by:
[tex]g(x)=|3x|+4[/tex]
Answer:
-12(x-4)
Step-by-step explanation:
I just took the test this is the answer!! Basically you take -3 and 4 and times it which would be -12. You then have x and another 4 left over. Since you are translating to the right you will be negative therefore giving us the answer -12(x-4).
